One of the most common goals of medical investigations is to determine if two or more populations are similar with respect to some attribute (or attributes) of interest. Of paramount interest in this study is the two-population problem, although we hope to have time to study the extension of some of the results to more than two populations. The overall objective of the project is to develop testing and estimation schemes that are partially sequential in nature. In particular, for the two-population setting, this means the sample size for the observations collected from one population is fixed, while the sample from the second population is collected sequentially, and thus has random sample size. However, these procedures will not be truly sequential, but will be truncated in the sense that there will be an upper bound on the (random) number of observations to be collected from the second population. Such schemes are able to capitalize on the best aspects of both fixed sample size and sequential procedures, and are particularly appropriate for many medical settings, as, for example, in the evaluation of a new treatment for a serious disease. BIBLIOGRAPHIC REFERENCES: Orban, J. and Wolfe, D. A. (1977). Properties of a distribution-free partially sequential two-sample median test. Submitted to J. Amer. Statist. Assoc. Wolfe, D. A (1977). Two-stage two-sample median test. Submitted to Technometrics.